⚛️ phenomenology

Entanglement entropy minimization and global symmetry violation in scatterings

This paper conjectures and provides evidence that the minimization of entanglement entropy in scattering processes acts as a selection principle that suppresses interactions violating global symmetries, thereby offering a potential information-theoretic explanation for the rarity of certain Beyond-the-Standard-Model phenomena.

Original authors: Shinya Kanemura, Masanori Tanaka

Published 2026-09-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Shinya Kanemura, Masanori Tanaka

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the subatomic world, particles do not merely bounce off one another like billiard balls; they interact in a way that weaves their identities together. When two particles collide, they can become "entangled," a state where the properties of one particle are inextricably linked to the other, no matter how far apart they drift. This is not a metaphor but a fundamental feature of quantum mechanics, a reality that has reshaped our understanding of information and the universe. For decades, physicists have studied the Standard Model, the best theory we have for how these particles behave, yet a lingering mystery remains: why are certain interactions, which would break the universe's most basic rules, so incredibly rare? Processes that violate the conservation of lepton number or baryon number, or that change the "flavor" of a particle in forbidden ways, are suppressed so heavily that they are nearly impossible to detect. Scientists have long suspected that new, hidden forces or high energy scales are to blame, but a deeper, more universal reason for this silence has remained elusive.

A team of researchers from the University of Osaka and Peking University has now proposed a new perspective on this silence, suggesting that the universe might simply prefer to keep things simple. They explored the idea that nature minimizes a specific kind of quantum complexity called entanglement entropy. In their view, when a particle collision occurs, the universe tends to settle into a state where the resulting quantum connections are as weak as possible. They hypothesized that this drive to minimize entanglement acts as a filter, naturally suppressing any interaction that would create a messy, highly entangled outcome. If this is true, the reason we do not see certain forbidden particle reactions is not just because the forces are weak, but because the universe's preference for low entanglement actively selects against them.

To test this idea, the researchers looked at several specific scenarios where the Standard Model's rules are broken. They examined processes where the total number of leptons, such as electrons and neutrinos, changes by two units, a violation that could explain why neutrinos have mass. They also looked at baryon number violation, which would allow a proton to decay, and flavor-changing processes where a particle suddenly switches its type, like a muon turning into an electron. In each case, they calculated the entanglement entropy generated by these hypothetical collisions. Their calculations revealed a striking pattern: whenever a symmetry-violating interaction opened a new channel for particles to scatter into, the state where that interaction was completely turned off became a local minimum for entanglement. In simpler terms, the universe's "preference" for low entanglement made the forbidden reactions less likely to happen, effectively pushing the probability of these events toward zero.

The researchers found that this effect was particularly robust when the new, forbidden channel involved particles that were fundamentally different from the allowed ones. For instance, if a collision could produce either two W bosons or two leptons, and these two outcomes occupied distinct, non-overlapping quantum spaces, the math showed that the entanglement was lowest when the lepton-producing channel was entirely absent. This held true for lepton number violation, baryon number violation, and flavor-changing neutral currents. The study suggests that the extreme rarity of these phenomena is not an accident of specific parameters but a consequence of a broader principle: the universe minimizes the quantum information generated in a collision. This minimization naturally favors the preservation of global symmetries, explaining why the universe appears so orderly and why certain dramatic events, like a proton spontaneously decaying, are so effectively suppressed.

However, the authors are careful to note that this principle is not a magic wand that forbids all violations. They point out that the effect depends on how the particles are measured and how their quantum states are defined. In some specific cases, such as when only one particle in a pair changes its flavor while the other stays the same, the conditions for this minimization are not met, and the suppression is not guaranteed. Furthermore, the study suggests a nuanced possibility for why we might still see tiny, non-zero effects at low energies. If the condition for minimum entanglement is met at a specific, high energy scale, it could force a cancellation between different types of interactions. This cancellation might not eliminate the effect entirely but could suppress it significantly as energy levels drop, leaving behind a faint, detectable signal that is much smaller than standard theories would predict. This offers a potential explanation for why experiments have set such tight limits on these processes without finding them, and why the universe might allow for a small, residual whisper of these forbidden interactions rather than a total silence.

Ultimately, this work proposes that the suppression of symmetry-violating phenomena is rooted in the information-theoretic structure of the universe itself. By treating particle collisions as sources of quantum information, the researchers have identified a mechanism where the drive to minimize entanglement acts as a guardian of the universe's symmetries. While the study does not prove that this is the sole reason for the absence of these events, it provides a compelling, unified framework that links the behavior of particles to the fundamental nature of quantum information. It suggests that the rules we observe in the Standard Model are not just arbitrary constraints but may be the result of a deeper tendency for the universe to organize itself in the most informationally efficient way possible.

Technical Summary: Entanglement Entropy Minimization and Global Symmetry Violation in Scatterings

Problem Statement
Despite the empirical success of the Standard Model (SM), the theoretical origin of the strong suppression of interactions that violate global symmetries (such as lepton number, baryon number, lepton flavor, and flavor-changing neutral currents) remains an open question. These suppressions are typically attributed to high new physics scales, small couplings, or specific parameter structures. This paper investigates whether a more general principle, rooted in quantum information theory, can explain the selection of symmetry-preserving interactions. Specifically, the authors examine the conjecture that the minimization of entanglement entropy (EE) generated in scattering processes systematically favors the suppression of symmetry-violating amplitudes.

Methodology
The authors employ a formalism defining EE in two-body scattering processes. The total Hilbert space is decomposed into kinetic and internal degrees of freedom (spin, particle type, color). The analysis focuses on the entanglement generated between two subsystems (e.g., the two outgoing momentum modes) after a scattering event.

Formalism: The initial state is a product state. The final state is a superposition of the SM contribution ( $|\psi_{SM}\rangle$ ) and a Beyond-the-Standard-Model (BSM) contribution ( $|\psi_{BSM}\rangle$ ) that violates a specific symmetry. The reduced density matrix $\rho_A$ is obtained by tracing out one subsystem.
Orthogonality Condition: The core of the argument relies on the condition where the SM and BSM sectors occupy different quantum-number sectors in the reduced Hilbert space. In such cases, the interference term in the reduced density matrix vanishes ( $\rho^{mix}_A = 0$ ), resulting in a block-diagonal structure.
Entropy Measure: The authors utilize linear entropy, $EE = 1 - \text{tr}(\rho_A^2)$ , as the measure of entanglement. They analyze the behavior of this entropy as a function of the relative weight $P$ of the symmetry-violating channel.
Application: The framework is applied to four representative BSM phenomena:
- Lepton Number Violation (LNV) via the Weinberg operator.
- Baryon Number Violation (BNV) relevant to proton decay.
- Lepton Flavor Violation (LFV) in charged lepton scattering.
- Flavor-Changing Neutral Currents (FCNC).

Key Contributions and Results

General Mechanism: The authors demonstrate that when a symmetry-violating interaction opens a final-state sector orthogonal to the symmetry-preserving sector (i.e., $\rho^{mix}_A = 0$ ), the symmetry-preserving point ( $P=0$ ) becomes a local minimum of the entanglement entropy. Consequently, the condition of minimum entanglement favors the suppression of the symmetry-violating amplitude.
Lepton Number Violation: Applied to $W^-W^- \to \ell^-\ell^-$ scattering induced by the Weinberg operator, the analysis shows that minimizing EE selects the lepton-number-conserving limit where the Weinberg operator and the corresponding $\Delta L = 2$ amplitude vanish. While a mathematical solution exists where only one neutrino has a nonzero mass, the authors note that this scenario is not plausible given neutrino oscillation data; thus, the minimization condition effectively predicts the absence of the LNV process.
Baryon Number Violation: For partonic scattering processes related to proton decay ( $uu \to \bar{d}e^+$ ), the orthogonality between the SM ( $uu \to uu$ ) and BNV sectors ensures that the BNV point is not a minimum. The minimum-entanglement condition favors $P_{BNV}=0$ , suggesting a mechanism for the extreme suppression of proton decay.
Lepton Flavor Violation: In charged lepton scattering where flavors are exchanged (e.g., $e^-\mu^+ \to e^+\mu^-$ ), the final states are locally orthogonal to the flavor-conserving states. The analysis confirms that the minimum-EE condition favors the suppression of these LFV amplitudes.
Flavor-Changing Neutral Currents: For processes like $q_i \bar{q}_j \to q_j \bar{q}_i$ , the orthogonality of flavor states leads to a block-diagonal density matrix. The flavor-conserving point is identified as a local minimum of EE, supporting the suppression of tree-level FCNCs.
Robustness: The authors verify that this result is robust under the choice of entanglement measure. Using von Neumann entropy, the symmetry-preserving point is shown to be an infinitely steep minimum, confirming that the suppression is not an artifact of using linear entropy.

Limitations and Nuances
The paper explicitly notes limitations to the generality of the argument:

Non-Orthogonal Cases: In LFV processes where only one of two lepton flavors changes (e.g., $|e^-\mu^+\rangle \to |e^-\mu^+\rangle$ with a flavor flip in one leg), the local orthogonality condition is not satisfied. In these cases, the interference term does not vanish, and the minimum-EE criterion does not guarantee a model-independent suppression of the amplitude.
Energy Scale Dependence: The minimization condition is defined for fixed kinematics. The authors propose that the condition $M_{BSM}=0$ might be realized at a specific characteristic energy scale $Q^*$ . If operators of different mass dimensions contribute, a cancellation at $Q^*$ can lead to a relation between Wilson coefficients (e.g., $C_6 \sim -C_8 Q^{*2}/\Lambda^2$ ). This mechanism could naturally suppress the leading BSM coefficient at low energies ( $Q \ll Q^*$ ) without requiring the interaction to be exactly zero, explaining the smallness of observed BSM effects.

Significance
The paper claims that the minimization of entanglement entropy provides a unified, information-theoretic principle underlying the suppression of various global symmetry-violating phenomena. By linking the suppression of BSM interactions to the orthogonality of final-state sectors in the Hilbert space, the work suggests that the "absence" of certain experimental signals (like proton decay or neutrinoless double-beta decay) may be a consequence of a fundamental tendency for scattering processes to minimize quantum entanglement. This offers a novel perspective on why nature might select symmetry-preserving limits, distinct from traditional explanations based solely on high mass scales or fine-tuned couplings.

Technical Summary: Entanglement Entropy Minimization and Global Symmetry Violation in Scatterings

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